Read e-book online Euler's Gem: The Polyhedron Formula and the Birth of PDF

By David S. Richeson

Leonhard Euler's polyhedron formulation describes the constitution of many objects--from football balls and gem stones to Buckminster Fuller's structures and sizeable all-carbon molecules. but Euler's formulation is so easy it may be defined to a toddler. Euler's Gem tells the illuminating tale of this crucial mathematical idea.

From old Greek geometry to trendy state of the art examine, Euler's Gem celebrates the invention of Euler's loved polyhedron formulation and its far-reaching influence on topology, the research of shapes. In 1750, Euler saw that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks ignored the formulation solely; how Descartes nearly came upon it yet fell brief; how nineteenth-century mathematicians widened the formula's scope in ways in which Euler by no means predicted by way of adapting it to be used with doughnut shapes, soft surfaces, and better dimensional shapes; and the way twentieth-century mathematicians chanced on that each form has its personal Euler's formulation. utilizing significant examples and various illustrations, Richeson provides the formula's many stylish and unforeseen functions, akin to exhibiting why there's consistently a few windless spot in the world, tips on how to degree the acreage of a tree farm by means of counting timber, and the way many crayons are had to colour any map.

packed with a who is who of extraordinary mathematicians who wondered, subtle, and contributed to a amazing theorem's improvement, Euler's Gem will fascinate each arithmetic enthusiast.

Show description

Read Online or Download Euler's Gem: The Polyhedron Formula and the Birth of Topology PDF

Best geometry & topology books

Read e-book online The Gelfand Mathematical Seminars, 1990–1992 PDF

This Seminar started in Moscow in November 1943 and has persisted with out interruption as much as the current. we're chuffed that with this vol­ ume, Birkhiiuser has began to post papers of talks from the Seminar. It was once, regrettably, tricky to arrange their ebook sooner than 1990. on the grounds that 1990, lots of the talks have taken position at Rutgers collage in New Brunswick, New Jersey.

Geometrie: Ein Lehrbuch für Mathematik- und - download pdf or read online

Für die Neuauflage dieses Buches, in dem für Mathematik- und Physikstudierende wichtiges geometrisches Verständnis und Wissen vermittelt wird, wurde der textual content behutsam verbessert und aktualisiert.

Get Classical Geometries in Modern Contexts: Geometry of Real PDF

The point of interest of this ebook and its geometric notions is on genuine vector areas X which are finite or limitless internal product areas of arbitrary measurement more than or equivalent to two. It characterizes either euclidean and hyperbolic geometry with recognize to common homes of (general) translations and basic distances of X.

Download e-book for kindle: Matrices and Graphs in Geometry (Encyclopedia of Mathematics by Miroslav Fiedler

Simplex geometry is a subject generalizing geometry of the triangle and tetrahedron. the proper instrument for its examine is matrix thought, yet purposes frequently contain fixing large platforms of linear equations or eigenvalue difficulties, and geometry can assist in visualizing the behaviour of the matter.

Extra info for Euler's Gem: The Polyhedron Formula and the Birth of Topology

Example text

Download PDF sample

Euler's Gem: The Polyhedron Formula and the Birth of Topology by David S. Richeson

by Michael

Rated 4.73 of 5 – based on 23 votes